Question: $ A = \left[\begin{array}{rr}-2 & -1\end{array}\right]$ $ D = \left[\begin{array}{rr}0 & 0\end{array}\right]$ Is $ A- D$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ A$ is of dimension $( m \times  n)$ and $ D$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ A$ ) must equal $ p$ (number of rows in $ D$ ) and 2. $ n$ (number of columns in $ A$ ) must equal $ q$ (number of columns in $ D$ Do $ A$ and $ D$ have the same number of rows? Yes Yes No Yes Do $ A$ and $ D$ have the same number of columns? Yes Yes No Yes Since $ A$ has the same dimensions $(1\times2)$ as $ D$ $(1\times2)$, $ A- D$ is defined.